Diffractive optical element including a diffractive grating pattern

ABSTRACT

Disclosed is a diffractive optical element which includes a diffractive grating pattern ion a base plate. The diffractive grating pattern includes a plurality of phase gratings arranged in parallel lines extending along a predetermined direction to cause diffraction of an incident beam. Each of the plurality of phase gratings has an asymmetrical phase pattern. There is a phase gap, ΔP, representing a phase difference (in radians) between an end point and a beginning point of each phase pattern. The phase gap, ΔP, is substantially equal for each of the plurality of phase gratings and satisfies the relationship. 
     
       
         0.7π&lt;|ΔP|&lt;1.2π.

This is a division of U.S. patent application Ser. No. 08/890,429, filedJul. 9, 1997, now U.S. Pat. No. 6,021,000 the contents of which areherein incorporated in its entirety.

BACKGROUND OF THE INVENTION

The present invention relates to a beam splitting optical element whichdivides an incident beam into a plurality of number of emitted beams,and more particularly, to a beam splitting optical element usingdiffractive gratings.

Conventionally, beam splitters using diffractive gratings have beenknown. In such beam splitters, linear grooves or raised portions (i.e.,gratings) are formed on, for example, a glass substrate. The arrangementof the gratings determines the pattern of emitted diffracted beams.Typically, the emitted beams (±1st order beams, ±2nd order beams, . . .) are arranged symmetrically around a central beam (i.e., a zero orderdiffracted beam) and, as a result, there are an odd number of diffractedbeams emitted.

A diffraction efficiency of the conventional diffractive gratings asdescribed above is generally in a range of 70%-85%. There is need for abeam splitter employing diffractive gratings which has a relatively highdiffraction efficiency.

Further, in the field of digital opto-electronics, it is particularlyuseful if a diffractive optical element has an even number of emittedbeams having relatively similar intensities. For example, in an opticalrecording device accessed by a computer or an optical computer, eightbits (a byte) is a unit when data is processed. If a beam is dividedinto an even and desired number of beams by the beam splitter, it isadvantageous since the emitted beams are used for processing the dataefficiently.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide animproved beam splitting optical element which divides an incident beaminto an even number of beams and has a higher diffraction efficiencythan a conventional element.

For the above object, according to one aspect of the invention, there isprovided a diffractive optical element, comprising a cylindrical surfaceprovided with a diffractive grating pattern. The diffractive gratingpattern includes a plurality of phase gratings arranged in parallellines extending along a circumference of the cylindrical surface tocause diffraction of an incident beam, where a beam incident on thediffractive grating pattern is emitted as divided into a plurality ofdiffracted beams. Since the grating pattern is formed on a cylindricalsurface, and the gratings extend along the circumference of thecylindrical surface, a mold to be used for molding the grating patterncan be made easily with use of, for example, a lathe.

Preferably, a surface of the optical element from which the diffractedbeams are emitted is also cylindrical having a curvature that issubstantially the same as a curvature of the cylindrical surface, sothat the phase diffracting element has a meniscus shape and hassubstantially no magnifying power in total.

Optionally, the plurality of phase gratings are of equal width in adirection of the generatrix of the cylinder and each of the plurality ofphase gratings has a continuous, nonlinear surface to cause phasedifferences in a wave front of the incident beam. The mold for such agrating can be made relatively easily when the lathe is used.

Further optionally, each of the plurality of phase gratings has anasymmetrical phase pattern, and a phase gap ΔP, representing a phasedifference between an end point of each of the plurality of phasepatterns and a beginning point of each of the plurality of phasepatterns, in radians. The phase gap, ΔP, is substantially equal for eachof the plurality of phase gratings and satisfies:

0.7π<|ΔP|<1.2π.

With this structure, the emitted beams (i.e., the diffracted beams)distribute asymmetrically with respect to the zero order diffractedbeam, and accordingly it is possible that the number of diffracted beamscan be adusted to an even number.

Further optionally, the plurality of phase gratings are adjusted so thateach of the divided diffracted beams have substantially the sameintensity and no divided beam is emitted other than the intended numberof beams. As a result, an even number of diffracted beams havingsubstantially the same intensity may be emitted from the diffractiveoptical element.

According to another aspect of the invention, there is provided adiffractive optical element, comprising a base plate provided with adiffractive grating pattern. The diffractive grating pattern includes aplurality of phase gratings arranged in parallel lines extending along apredetermined direction of the base plate to cause diffraction of anincident beam. A beam incident on the diffractive grating pattern isemitted as a plurality of diffracted beams, wherein each of theplurality of phase gratings has an asymmetrical phase pattern in adirection where the plurality of phase gratings are arranged. A phasegap ΔP, representing a phase difference between an end point of each ofthe plurality of phase patterns and a beginning point of each of theplurality of phase patterns, in radians, is substantially equal for eachof the plurality of phase gratings and satisfies:

0.7π<|ΔP|<1.2π.

With this optical element, a desired even number of diffracted beams,which are asymmetrically distributed with respect to the zero orderbeam, are obtained.

It should be noted that the diffracted beams substantially consist of adesired number of beams.

Various examples are indicated as embodiments. In each embodiment, apredetermined error in the phase pattern is permissible.

Specifically, the predetermined permissible error in the phasedifference may be less than 2%.

According to a further aspect of the invention, there is provided adiffractive optical element, comprising: a base plate having acylindrical surface; and a diffractive grating pattern engraved on thecylindrical surface in a direction perpendicular to a generatrix of thecylindrical surface so that diffracted beams distribute in a dimensionalong the generatrix.

Since the diffractive grating pattern is formed on the cylindricalsurface, a mold to be used for molding the optical element can beproduced relatively easily.

Optionally, the grating pattern includes a plurality of phase gratings.Due to the shape of the optical element, and therefore the shape of themold for the optical element, a complicated pattern can be employed.Accordingly, the grating can be a phase grating. When employing thechase grating, diffraction efficiency is improved.

Optionally or alternatively, each of the phase gratings has anasymmetrical phase pattern. As a result, the diffracted beams distributeasymmetrically with respect to a zero order diffracted beam.

Accordingly, by selecting an appropriate phase pattern of the phasegratings, an even number of diffracted beams can be emitted.

According to a further aspect of the invention, there is provided amethod for producing a diffracting optical element, comprising: making amold by (1) rotating a cylindrical metal mold about a rotation axis, and(2) moving a cutting tool to a predetermined radial distance from therotation axis and moving the tool along the rotation axis; and applyingan injection mold process with use of a master made by the steps ofmaking the mold to make the diffracting optical element.

With this method, a complicated phase pattern can be formed on the mold.

According to a further aspect of the invention, there is provided amethod for producing a mold to be used for making a diffracting opticalelement having a cylindrical surface with an injection mold process,comprising (1) rotating a cylindrical metal mold about a rotation axis,add (2) moving a cutting tool to a predetermined radial distance fromthe rotation axis and moving the tool along the rotation axis. Also withthis method, a complicated pattern extending along a circumference ofthe mold can be formed on the circumferential surface of the mold.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic enlarged perspective view of gratings formed on abeam splitter according to an embodiment of the invention;

FIG. 2 is a perspective view of the beam splitter according to anembodiment of the invention;

FIG. 3 is a perspective view illustrating a process for making a moldfor the beam splitter of FIG. 2;

FIGS. 4 through 15 are graphs illustrating exemplary phase patterns forthe beam splitter of FIG. 2;

FIGS. 16 through 27 are graphs showing a distribution of intensities ofthe diffracted beams corresponding to the exemplary phase patterns ofFIGS. 4 through 15; and

FIG. 28 is a perspective view of the beam splitter according to analternative embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 2 is a perspective view of a bean splitter 10 according to anembodiment of the invention. The beam splitter 10 includes a base 11 onwhich a grating pattern 12 is formed. As shown in FIG. 2, the base 11has a concave surface 11 a and a convex surface 11 b and is representedas a portion of a wall of a cylinder. In FIG. 2, dotted lines show animaginary cylinder with ends C1 and C2 having equal diametersrepresenting a diameter of the concave surface 11 a. The grating pattern12 is formed on the concave surface 11 a.

FIG. 1 is a schematic enlarged view of the grating pattern 12. It shouldbe noted that in FIG. 1, the grating pattern 12 is shown as formed on aflat surface, and description with reference to FIG. 1 is made as if thegrating pattern 12 is formed on the flat surface. As described above,however, the grating pattern 12 is actually formed on the concavesurface 11 a.

The grating pattern 12 is formed having a plurality of identicallyformed phase gratings P extending linearly. Each of the phase gratings Phave a predetermined length L along a y-axis direction and linearlyextend in an x-axis direction. In particular, the phase gratings shownin FIG. 1 correspond to a particular numerical example (example 3)described in more detail below. Note that the y-axis direction is adirection parallel to a generatrix of the base 11 (i.e., the imaginarycylinder defined by the end circles C1 and C2) and the x-axis directionrepresents the curve of the concave surface 11 a.

The grating pattern 12 and the base 11 are made of, for example, glassor a transparent resinous material. The grating pattern 12 is formed sothat it divides an incident beam into a plurality of diffracted emittedbeams. It should be noted that the grating pattern can be formed on aflat surface. Practically, however, due to difficulty in producing acomplicated grating pattern as described below, it is preferable toemploy a cylindrical surface as a surface on which the grating pattern12 is formed. Further, if the cylindrical surface is employed, it may beadvantageous to use resinous material for the optical element, and theoptical element may be formed with a molding process.

As shown in FIG. 1, a cross section along a Y-Z plane of each phasegrating P has a shape which causes non-linear beams to pass therethroughalong directions represented by the arrows D, E in FIG. 2. In otherwords, lines representative of the phase difference caused by the beamsplitter 10 is similar to the cross-sectional shape of the phasegratings P. If the phase difference caused by the grating is representedby δ with respect to the lowermost portion of the surface of the phasegrating P, the surface of the phase grating P is defined by a non-linearphase difference δ which varies along the y-axis direction. In otherwords, the phase difference δ is defined as a difference between a pointon a phase grating P and a predetermined reference point on the phasegrating P. In the embodiments, the predetermined reference point isdetermined and meets with an adjacent phase grating P with a phase gapΔP. In particular, the phase gap ΔP should be constant for all phasegratings P and should satisfy the condition:

0.7π<|ΔP|<1.2π.

According to the beam splitter 10 of the embodiment, the cross-sectionalong the y-axis phase gratings P have an asymmetrical, shape (i.e., anasymmetrical phase distribution), and the diffracted beams are alsoasymmetrical with respect to a zero order diffracted beam and theincident beam is divided into an even number of emitted beams.

A method of forming the beam splitter 10 is now described. Since thecross-sectional shape of the phase patterns P is nonlinear andcomplicated, it is difficult to form a mold for the grating pattern 12using an etching process. Accordingly, the diffractive optical element10 is molded using a metal mold. However, if the surface on which amaster pattern is formed is a flat surface, a cutting tool for formingthe pattern is to be moved three dimensionally, i.e., in the x, y and zaxis directions relative to the surface. Considering the size of thegratings, it may be very difficult to control the movement of thecutting tool to form the pattern precisely.

FIG. 3 is a perspective view illustrating a process for making a mold 30for the beam splitter 10. Since each of the gratings has a surface whichcannot be made with use of an etching or the like, the mold 30 should beused in order to make the phase gratings. The mold 30 is a cylindricalmember as shown in FIG. 2, and the pattern 31, representing the gratingpattern 12, is formed on the circumferential surface of the mold 30using a cutting tool 100. The mold 30 is then used to form the beamsplitter 10 hen the beam splitter 10 is made, for example, a well-knowninjection mold method is applied using the mold 30 as a master. Itshould be noted that the beam splitter 10 is formed of optical plasticsuch as PMMA (Plymethyl methacrylate).

In this embodiment, as shown in FIG. 2, since the phase difference δ ofeach phase pattern P is constant along the x-axis direction, thepositional relation between the mold 30 and the cutting tool 100 needonly be adjusted in two dimensions (i.e., the y-axis direction and thez-axis direction). Thus, the phase patterns P can be engraved accuratelyin a short time and at a low cost.

As shown in FIG. 3, the cutting tool 100 includes a lathe 20, a support21 rotated by the lathe 20 and movable along a rotation axis thereof(i.e., movable in a y-axis direction), a sliding table 22 arranged tomove perpendicular to the rotation axis of the support 21 (i.e., in az-axis direction), and a tool 23 fixedly provided on the sliding table22.

The metal mold 30 is fixed coaxially with the support 21 and is rotatedin a direction Rx (corresponding; to the x-axis direction of FIG. 1).Then, by appropriate movement of the support 21 along the y-axisdirection and of the sliding table 22 along the z-axis direction withthe metal mold 30 rotated, the mold 30 for the phase gratings P isformed.

The mold formed 30 is then used to form the beam splitter 10.

Twelve particular numerical examples of the phase grating P are nowdescribed with reference to FIGS. 4 through 27.

In example 1, the phase grating P is formed such that an incident beamis divided into 4 emitted beams by the beam splitter 10, in examples2-5, the phase grating P is formed such that an incident beam is dividedinto 8 emitted beams, and in examples 6-12, the phase grating P isformed such that an incident beam is divided into 16 emitted beams bythe beam splitter 10.

In these examples, the phase grating P is designed such that: (1)intensities of each emitted beam are substantially the same, and (2)only the intended number of emitted beams are emitted. In the followingdescription, the width L (i.e., the length of in the Y-axis direction)of each phase grating p is divided into 64 co-ordinates (designated0-63). A reference point is designated as a point at which the phasepattern P is lowest in relation to the concave surface 11 a. Further,the phase difference δ for each co-ordinate is given in radians.Accordingly, the phase difference δ is more than 0. However, a height Halong the z-axis direction (i.e., an actual height of the phase grating)in micrometers (μm) may be calculated, for a predetermined incidentbeam, using the formula:

H=δ×λ/(2π(n−1)),

where n is a refractive index of the material of the beam splitter 10and λ is a wavelength of the incident beam. It is assumed that the beamsplitter 10 is located within air whose refractive index is regarded as1.

EXAMPLE 1

Table 1 shows data for a pattern of the phase grating P according toexample 1. The data is shown graphically in FIG. 4 where a vertical axisis the phase difference δ and a horizontal axis is the coordinate alongthe y-axis direction. In example 1, the phase gap ΔP is 1.00π. Notethat, the phase gap ΔP is defined as a difference between the phases atthe coordinate 0 and the coordinate 63.

TABLE 1 (ΔP = 1.00π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 2.28947 442.89397 1 0.04000 23 2.51947 45 2.79397 2 0.10042 24 2.69518 46 2.742793 0.16042 25 2.86518 47 2.69279 4 0.21520 26 3.02656 48 2.67291 50.25520 27 3.14656 49 2.65291 6 0.32315 28 3.25191 50 2.66056 7 0.3831529 3.35191 51 2.67056 8 0.44920 30 3.41679 52 2.67518 9 0.51920 313.48679 53 2.69518 10 0.59142 32 3.52997 54 2.72447 11 0.66142 333.55997 55 2.75447 12 0.75100 34 3.59951 56 2.79033 13 0.84100 353.59951 57 2.82033 14 0.94020 36 3.58770 58 2.86386 15 1.05020 373.55770 59 2.89386 16 1.17834 38 3.50415 60 2.94434 17 1.30834 393.44415 61 2.98434 18 1.46586 40 3.33870 62 3.03420 19 1.64586 413.21870 63 3.13420 20 1.84933 42 3.10951 21 2.06933 43 2.96951

EXAMPLE 2

Table 2 shows data for a pattern of the phase grating P according toexample 2. The data is shown graphically in FIG. 5. In example 2, thephase gap ΔP is 0.75π.

TABLE 2 (ΔP = 0.75) Coord. δ Coord. δ Coord. δ 0 2.34750 22 2.33100 446.16100 1 2.11350 23 2.54700 45 6.29850 2 2.10350 24 2.76700 46 6.388503 2.11700 25 2.98600 47 6.46600 4 2.13200 26 3.23600 48 6.51600 52.14700 27 3.57850 49 6.53700 6 2.14700 28 4.10850 50 6.48700 7 2.1035029 4.68100 51 6.38100 8 1.96350 30 5.10100 52 6.17100 9 1.32750 315.39450 53 5.85000 10 0.36750 32 5.57450 54 5.47000 11 0.07000 335.70650 55 5.22600 12 0.00000 34 5.79650 56 5.06600 13 0.02550 355.84250 57 4.99800 14 0.12550 36 5.88250 58 4.94800 15 0.23800 375.89250 59 4.93550 16 0.40800 38 5.89250 60 4.92550 17 0.65600 395.89650 61 4.91000 18 0.96600 40 5.90650 62 4.89000 19 1.34000 415.91450 63 4.70250 20 1.72000 42 5.96450 21 2.05100 43 6.06100

EXAMPLE 3

Table 3 shows data for a pattern of the phase grating P according toexample 3. The data is shown graphically in FIG. 6. In example 3, thephase gap ΔP is 0.99π.

TABLE 3 (ΔP = 0.99π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 5.53800 445.95500 1 0.04000 23 5.69800 45 5.74500 2 0.08700 24 5.81200 46 5.574003 0.16700 25 5.87200 47 5.43400 4 0.24600 26 5.88400 48 5.33000 50.35600 27 5.85400 49 5.23000 6 0.45900 28 5.78500 50 5.11400 7 0.6390029 5.70500 51 4.94400 8 0.88800 30 5.63700 52 4.63400 9 1.31800 315.63700 53 4.11400 10 1.99700 32 5.67800 54 3.52200 11 2.65700 335.79800 55 3.20200 12 3.03300 34 5.95300 56 3.03800 13 3.30300 356.12300 57 2.95800 14 3.52200 36 6.28800 58 2.94800 15 3.71200 376.41800 59 5.98500 16 3.91200 38 6.51300 60 2.96900 17 4.15200 396.55300 61 2.98900 18 4.41000 40 6.53000 62 3.03300 19 4.73000 416.47000 63 3.09800 20 5.03600 42 6.35300 21 5.32600 43 6.16300

EXAMPLE 4

Table 4 shows data for a pattern of the phase grating P according toexample 4. The data is shown graphically in FIG. 7. In example 4, thephase gap ΔP is 0.99π.

TABLE 4 (ΔP = 0.99π) Coord. δ Coord. δ Coord. δ 0 1.57900 22 2.15900 442.38400 1 1.63900 23 2.39900 45 2.11400 2 1.66700 24 2.60700 46 1.932003 1.69700 25 2.81700 47 1.81200 4 1.73900 26 3.04600 48 1.74600 51.74400 27 3.25600 49 1.75600 6 1.73000 28 3.49200 50 1.82500 7 1.7000029 3.71200 51 1.96500 8 1.55400 30 3.90500 52 2.26500 9 1.25400 314.02500 53 2.82500 10 0.71100 32 4.06700 54 3.47800 11 0.25100 334.04700 55 3.87800 12 0.05000 34 3.97200 56 4.09500 13 0.00000 353.84200 57 4.23500 14 0.04100 36 3.70100 58 4.34700 15 0.12100 373.57100 59 4.43700 16 0.28200 38 3.44500 60 4.50400 17 0.50200 393.33500 61 4.55400 18 0.80200 40 3.22000 62 4.62600 19 1.15200 413.09000 63 4.68600 20 1.52900 42 2.90600 21 1.87900 43 2.65600

EXAMPLE 5

Table 5 shows data for a pattern of the phase grating P according toexample 5. The data is shown graphically in FIG. 8. In example 5, thephase gap ΔP is 1.00λ.

TABLE 5 (ΔP = 1.00π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 5.13656 445.80812 1 0.03494 23 5.21307 45 5.60323 2 0.08372 24 5.20778 46 5.379183 0.17593 25 5.13788 47 5.12460 4 0.29127 26 4.97072 48 4.88807 50.41957 27 4.73558 49 4.68950 6 0.57022 28 4.48842 50 4.48952 7 0.7790829 4.32697 51 4.29759 8 1.04067 30 4.24668 52 4.05168 9 1.33889 314.24576 53 3.80124 10 1.70048 32 4.27485 54 3.56782 11 2.04910 334.39394 55 3.34777 12 2.38318 34 4.58241 56 3.19436 13 2.68329 354.84203 57 3.08368 14 2.97144 36 5.19737 58 3.01120 15 3.26819 375.51068 59 2.97107 16 3.58289 38 5.77602 60 2.96391 17 3.93565 395.94409 61 2.98987 18 4.28787 40 6.03755 62 2.99927 19 4.60094 416.07922 63 3.13750 20 4.85049 42 6.05674 21 5.03591 43 5.96950

EXAMPLE 6

Table 6 shows data for a pattern of the phase grating P according toexample 6. The data is shown graphically in FIG. 9. In example 6, thephase gap ΔP is 1.01π.

TABLE 6 (ΔP = 1.01π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 9.01142 447.39884 1 0.11909 23 9.28050 45 7.47793 2 0.38167 24 9.40910 46 7.703023 0.86576 25 9.51318 47 8.32711 4 1.60085 26 9.57577 48 8.88019 52.24994 27 9.42985 49 8.91927 6 2.70552 28 8.82495 50 8.63937 7 3.1546129 8.55903 51 8.24345 8 3.79220 30 8.57712 52 7.86954 9 4.65129 318.64120 53 7.49862 10 5.33787 32 8.69029 54 6.90022 11 5.83696 338.68438 55 6.09930 12 6.33905 34 8.73447 56 5.52989 13 6.84314 359.13856 57 5.20897 14 7.22122 36 9.91164 58 4.85157 15 7.25031 3710.12573 59 4.33065 16 6.79540 38 10.16132 60 3.66374 17 6.30948 3910.14541 61 3.27782 18 6.15257 40 10.08499 62 3.13342 19 6.17165 419.91408 63 3.17750 20 6.27975 42 8.31967 21 7.34883 43 7.42876

EXAMPLE 7

Table 7 shows data for a pattern of the phase grating P according toexample 7. The data is shown graphically in FIG. 10. In example 7, thephase gap ΔP is 0.98π.

TABLE 7 (ΔP = 0.98π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 9.18279 448.33523 1 0.10112 23 9.81372 45 7.85733 2 0.21482 24 10.31935 46 7.253753 0.46317 25 10.74935 47 6.51311 4 0.87331 26 11.07071 48 5.96011 51.39192 27 11.23482 49 5.55847 6 1.73829 28 11.08046 50 5.07889 71.78828 29 10.43581 51 4.47400 8 1.74891 30 9.96051 52 4.01530 9 1.6898431 9.86263 53 3.87218 10 1.76142 32 9.91072 54 3.90177 11 2.02072 3310.11877 55 4.04902 12 2.55159 34 10.68425 56 4.20056 13 3.28166 3511.42907 57 4.21774 14 3.83542 36 11.68461 58 4.00155 15 4.34223 3711.60267 59 3.56311 16 4.99540 38 11.38748 60 3.24915 17 5.83822 3911.05666 61 3.11798 18 6.55497 40 10.65121 62 3.08845 19 7.10304 4110.11445 63 3.09300 20 7.68791 42 9.43005 21 8.41221 43 8.81092

EXAMPLE 8

Table 8 shows data for a pattern of the phase grating P according toexample 8. The data is shown graphically in FIG. 11. In example 8, thephase gap ΔP is 1.14π.

TABLE 8 (Δ P = 1.14) Coord. δ Coord. δ Coord. δ  0 0.00000 22 8.14593 446.38976  1 0.35675 23 8.06924 45 6.15963  2 0.59145 24 7.78458 465.82247  3 1.02421 25 7.15265 47 5.41843  4 1.76643 26 6.44611 484.98783  5 2.45950 27 5.97778 49 4.50606  6 2.97905 28 5.63530 504.05856  7 3.46447 29 5.27806 51 3.78350  8 4.30512 30 4.81668 523.74228  9 5.26163 31 4.14179 53 4.15449 10 5.78634 32 3.46774 545.00983 11 6.07644 33 3.08316 55 5.34813 12 6.23928 34 2.88663 565.39878 13 6.33414 35 2.84806 57 5.22764 14 6.27698 36 3.03808 584.60923 15 6.11553 37 3.51615 59 3.77745 16 5.97524 38 4.17204 603.46904 17 5.92432 39 4.54980 61 3.39766 18 6.05341 40 4.92638 623.41174 19 6.40250 41 5.62633 63 3.59185 20 7.41097 42 6.27292 218.03059 43 6.49224

EXAMPLE 9

Table 9 shows data for a pattern of the phase grating P according toexample 9. The data is shown graphically in FIG. 12. In example 9, thephase gap ΔP is 0.86π.

TABLE 9 (ΔP = 0.86π) Coord. δ Coord. δ Coord. δ 0 0.00000 22 10.41512 4411.31028 1 0.02139 23 10.45448 45 11.04914 2 0.24455 24 10.66319 4610.70583 3 0.63197 25 11.05519 47 10.49409 4 1.25970 26 11.52474 4810.31520 5 1.93395 27 11.90449 49 10.09816 6 2.45426 28 12.17922 509.41989 7 2.94875 29 12.38914 51 8.18725 8 3.67947 30 12.57125 527.75399 9 4.63407 31 12.71915 53 7.51219 10 5.28644 32 12.78723 547.14200 11 5.75541 33 12.73151 55 6.22557 12 6.29385 34 12.67358 565.34703 13 7.22466 35 12.59483 57 4.96071 14 8.10410 36 12.48228 584.61458 15 8.59831 37 12.25170 59 4.07851 16 8.96738 38 11.83332 603.42295 17 9.36434 39 11.38850 61 3.06471 18 9.85078 40 11.15996 622.90472 19 10.26310 41 11.13878 63 2.69100 20 10.46203 42 11.22934 2110.45751 43 11.33304

EXAMPLE 10

Table 10 shows data for a pattern of the phase grating P according toexample 10. The data is shown graphically in FIG. 13. In example 10, thephase gap ΔP is 1.07π.

TABLE 10 (ΔP = 1.07π) Coord. δ Coord. δ Coord. δ 0 1.88359 22 6.11453 440.00000 1 2.20660 23 5.47716 45 0.11027 2 2.55505 24 4.92379 46 0.553343 2.96194 25 4.32768 47 1.03784 4 3.50884 26 3.82595 48 1.31994 54.12613 27 3.35523 49 1.57085 6 4.76767 28 2.90596 50 1.87626 7 5.4782229 2.32512 51 2.43060 8 6.13673 30 1.74405 52 3.02974 9 6.68710 311.41813 53 3.35112 10 7.20112 32 1.33906 54 3.36775 11 7.89495 331.50709 55 3.30493 12 9.04040 34 1.88758 56 3.22809 13 9.57330 352.18736 57 3.38151 14 9.71868 36 2.27226 58 3.63778 15 9.62977 372.04002 59 3.99318 16 9.28356 38 1.53403 60 4.32386 17 8.61084 391.01003 61 4.56700 18 8.05756 40 0.69457 62 4.81525 19 7.66091 410.47837 63 5.24823 20 7.25906 42 0.31341 21 6.74087 43 0.09924

EXAMPLE 11

Table 11 shows data for a pattern of the phase grating P according toexample 11. The data is shown graphically in FIG. 14. In example 11, thephase gap ΔP is 1.04π.

TABLE 11 (ΔP = 1.04π) Coord. δ Coord. δ Coord. δ 0 5.72434 22 3.36629 442.81337 1 5.63396 23 3.48561 45 3.34012 2 5.50930 24 3.42313 46 3.804823 5.27261 25 3.12300 47 4.35758 4 4.88795 26 2.69584 48 4.96980 54.30602 27 2.35180 49 5.69287 6 3.64948 28 1.99120 50 6.46242 7 3.0811529 1.63443 51 7.23784 8 2.55867 30 1.17193 52 7.81849 9 1.97143 310.85687 53 8.30500 10 1.34005 32 0.75565 54 8.79971 11 0.79516 330.92786 55 9.44981 12 0.40111 34 1.14320 56 9.93265 13 0.10653 351.34150 57 10.15751 14 0.00000 36 1.34215 58 10.06035 15 0.05143 371.13101 59 9.80890 16 0.39145 38 0.74260 60 9.48861 17 0.97952 390.50082 61 9.27769 18 1.48361 40 0.45241 62 9.11678 19 1.93317 410.64103 63 8.98587 20 2.36975 42 1.08511 21 2.92970 43 2.01522

EXAMPLE 12

Table 12 shows data for a pattern of the phase grating P according toexample 12. The data is shown graphically in FIG. 15. In example 12, thephase gap ΔP is 0.98π.

TABLE 12 (ΔP = 0.98π) Coord. δ Coord. δ Coord. δ 0 1.54498 22 5.12490 444.58932 1 1.53807 23 5.76799 45 4.08540 2 1.47715 24 6.51557 46 3.648503 1.24424 25 7.20367 47 3.38558 4 0.73233 26 7.74924 48 3.32567 50.22242 27 8.19234 49 3.45876 6 0.00000 28 8.70042 50 3.70385 7 0.0470829 9.36852 51 3.91694 8 0.38968 30 9.97109 52 3.97602 9 1.19776 3110.29019 53 3.83511 10 1.79235 32 10.33327 54 3.20469 11 1.98643 3310.09636 55 2.54279 12 1.97353 34 9.53795 56 2.38836 13 1.83361 358.96804 57 2.49146 14 1.66370 36 8.57712 58 2.85804 15 1.65178 378.20621 59 3.52314 16 1.84488 38 7.75680 60 4.08221 17 2.25997 397.15388 61 4.39631 18 2.82905 40 6.55447 62 4.55539 19 3.44314 416.03255 63 4.60899 20 4.01223 42 5.55515 21 4.55932 43 5.07323

Tables 13 and 14 show the output intensity for the emitted beams of thebeams splitter 10 in each of the above twelve examples as a relativeintensity when the intensity of the incident beam is defined as 1.Further, an effective intensity represents a sum of the intensities ofthe intended emitted beams as a percentage of the incident beam. Asexplained above, the intended emitted beams are, for example, in example1, the four emitted beams of order −1 to +2, or in example 2, the eightemitted beams of order −3 to +4.

FIGS. 16-27 show the data of Tables 13 and 14 graphically, thehorizontal axis represents the order of the emitted diffracted beam andthe vertical axis represents the intensity of each order where theintensity of the incident beam is defined as 1.

TABLE 13 Order Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 −10 0.00097 0.003960.00162 0.00142 0.00142 0.00123 −9 0.00113 0.00850 0.00503 0.005260.00136 0.00568 −8 0.00126 0.00762 0.00528 0.00273 0.00244 0.00207 −70.00207 0.00171 0.00186 0.00440 0.00068 0.05752 −6 0.00257 0.000930.00023 0.00048 0.00513 0.05869 −5 0.00201 0.00156 0.00039 0.000910.00011 0.05867 −4 0.00874 0.00584 0.00316 0.00175 0.00007 0.05900 −30.01013 0.11779 0.11830 0.11805 0.12016 0.05797 −2 0.00226 0.119170.11781 0.11865 0.11955 0.05872 −1 0.22965 0.11753 0.11965 0.119490.12001 0.05928 0 0.23019 0.11745 0.11878 0.11879 0.12056 0.05975 10.23039 0.11841 0.11876 0.11903 0.12045 0.05970 2 0.22923 0.117170.11962 0.11942 0.11997 0.05907 3 0.00231 0.11643 0.11770 0.118590.11957 0.05875 4 0.01049 0.11663 0.11824 0.11794 0.12017 0.05798 50.00898 0.00126 0.00320 0.00174 0.00004 0.05911 6 0.00213 0.004620.00046 0.00092 0.00019 0.05861 7 0.00282 0.00004 0.00022 0.000560.00550 0.05882 8 0.00225 0.00227 0.00184 0.00444 0.00073 0.05750 90.00137 0.00003 0.00521 0.00279 0.00263 0.00253 10 0.00133 0.003970.00499 0.00527 0.00158 0.00658 Effec. 91.95% 94.06% 94.89% 95.00%96.04% 93.91%

TABLE 14 Order Ex. 7 Ex. 8 Ex. 9 Ex. 10 Ex. 11 Ex. 12 −10 0.001650.00019 0.00024 0.00004 0.00052 0.00020 −9 0.00089 0.00053 0.000020.00106 0.00117 0.00017 −8 0.00457 0.00028 0.00292 0.00098 0.000280.00092 −7 0.06045 0.05997 0.06068 0.06070 0.06086 0.06125 −6 0.060560.06019 0.06117 0.06027 0.06086 0.06103 −5 0.06008 0.06018 0.061260.06076 0.06076 0.06091 −4 0.06037 0.05995 0.06077 0.06038 0.060970.06116 −3 0.06089 0.06015 0.06083 0.06078 0.06078 0.06105 −2 0.060330.06017 0.06074 0.06065 0.06085 0.06115 −1 0.06028 0.06058 0.060700.06044 0.06101 0.06122 0 0.06020 0.06056 0.06061 0.06092 0.061160.06107 1 0.06023 0.06050 0.06051 0.06082 0.06092 0.06105 2 0.060220.06060 0.06043 0.06087 0.06099 0.06113 3 0.06041 0.06108 0.060630.06111 0.06106 0.06115 4 0.06087 0.06074 0.06066 0.06119 0.061000.06095 5 0.06037 0.06055 0.06053 0.06127 0.06107 0.06110 6 0.060080.06092 0.06091 0.06057 0.06129 0.06093 7 0.06055 0.06035 0.060830.06116 0.06104 0.06102 8 0.06041 0.06129 0.06032 0.06099 0.061200.06118 9 0.00463 0.00144 0.00115 0.00113 0.00173 0.00111 10 0.000860.00187 0.00028 0.00021 0.00035 0.00026 Effec 96.63% 96.78% 97.16%97.29% 97.58% 97.74%

As shown in table 13 and 14, the effective intensity of the intendedemitted beams is more than 91% in each example and reaches as high as97.74%.

Tables 15 and 16 show the intensity of the intended emitted beams as apercentage of an ideal value. For instance, in example 1, the idealvalue of each emitted beam is 0.25 (4 emitted beams are desired) wherethe intensity of the incident beam is 1, however, the actual intensityof the emitted beam of −1 order is 0.22965 so that the percentage of the−1 order beam is 92%. Similarly, the ideal values are 0.125 in examples2-4 (8 emitted beams are desired) and 0.0625 in examples 6-12 (16emitted beams are desired).

TABLE 15 Order Ex. 1 Ex. 2 Ex. 3 Ex. 4 Ex. 5 Ex. 6 −7 92% −6 94% −5 94%−4 94% −3 94% 95% 94% 96% 93% −2 95% 94% 95% 96% 94% −1 92% 94% 96% 96%96% 95% 0 92% 94% 95% 95% 96% 96% 1 92% 95% 95% 95% 96% 96% 2 92% 94%96% 96% 96% 95% 3 93% 94% 95% 96% 94% 4 93% 95% 94% 96% 93% 5 95% 6 94%7 94% 8 92% Δ  0%  2%  2%  2%  0%  4%

TABLE 16 Order Ex. 7 Ex. 8 Ex. 9 Ex. 10 Ex. 11 Ex. 12 −7 97% 96% 97% 97%97% 98% −6 97% 96% 98% 96% 97% 98% −5 96% 96% 98% 97% 97% 97% −4 97% 96%97% 97% 98% 98% −3 97% 96% 97% 97% 97% 98% −2 97% 96% 97% 97% 97% 98% −196% 97% 97% 97% 98% 98% 0 96% 97% 97% 97% 98% 98% 1 96% 97% 97% 97% 97%98% 2 96% 97% 97% 97% 98% 98% 3 97% 98% 97% 98% 98% 98% 4 97% 97% 97%98% 98% 98% 5 97% 97% 97% 98% 98% 98% 6 96% 97% 97% 97% 98% 97% 7 97%97% 97% 98% 98% 98% 8 97% 98% 97% 98% 98% 98% Δ  1%  2%  1%  2%  1% 1%

As shown in Tables 15 and 16, the intensities of the intended emittedbeams are in a range of 92%-98% in all examples. Further, a difference Δbetween maximum and minimum percentage values is at most 4%.Accordingly, in these examples, the energy of the incident beam iseffectively equally divided among the intended emitted beams.

The intensities shown in the above Tables and Figures represent idealvalues. In considering some errors in the beam diffractive element, theefficiency will be reduced. In particular, if the error in theefficiency is to be under 10%, the permissible error in the pattern ofthe phase grating P is about 2%. For examples if the refractive index nof the environment is 1.5, the incident beam has a wavelength λ of 488nm and is to be divided into 8 emitted beams every 0.0125 rad, thepattern has a length L along the axis of about 40 μm and a maximumheight H along the z-axis of about 1 μm. Here, the height H is definedas a difference between the highest and the lowest points in the phasepattern P. Thus, the permissible error in the height is only 0.02 μm.

However, the permissible error range can be extended. For example, if adifference between the refractive indexes of the phase grating P and theenvironment is decreased, the size of the phase pattern can beincreased. That is, if the difference between refractive indexes issmaller, the height H can be larger. Accordingly, the requiredprocessing precision of the beam splitter 10 can be reduced. In aparticular case, the concave surface 11 a, including the grating pattern12, may be covered with a liquid layer having a refractive index that isalmost equal to that of the grating pattern 12.

As described above, in each embodiment, the grating pattern isasymmetrical in the direction where the gratings are aligned. Thus thediffracted beams are not symmetrical with respect to zero order beam,and an even number of diffracted beams are generated. Further, thediffraction efficiency is raised by forming the grating pattern to havemulti-level phase distribution, and energy of the incident beam isefficiently used.

It should be noted that the phase patterns described above should beoptimized so that the diffracted beams consist substantially of adesired number (even number) of beams, and the desired number of beamshave substantially the same intensities.

Although the structure and operation of a beam splitter is describedherein with respect to the preferred embodiments. Many modifications andchanges can be made without departing from the spirit and scope of theinvention.

For example, as an alternative, the phase patterns P may be formed assubstantially indenting into the base 11 (as shown in FIG. 28) ratherthan as substantially protruding from the base 11 (as shown in FIG. 2).For examples given above, the alternative forms for the phase patterns Pcan be obtained if the reference point (i.e., the 0 point) remains thesame but each of the phase differences δ are defined as negative values.In other words, the cross-section of the phase pattern in the Y-Z planecan be considered to be rotated about the Y-axis by 180 degrees toproduce a mirror image of the phase pattern.

The present disclosure relates to subject matter contained in JapanesePatent Application Nos. HEI 08-198271, filed on Jul. 9, 1996, and HEI08-198272, filed on Jul. 9, 1996, which are expressly incorporatedherein by reference in their entirety.

What is claimed is:
 1. A diffractive optical element, comprising acylindrical surface provided with a diffractive grating pattern, saiddiffractive grating pattern including a plurality of phase gratingsarranged in parallel lines extending along a circumference of saidcylindrical surface to cause diffraction of an incident beam, wherein abeam incident on said diffractive grating pattern is divided and emittedinto a plurality of diffracted beams; wherein a surface of said opticalelement from which said diffracted beams are emitted is cylindricalhaving a curvature that is substantially the same as a curvature of saidcylindrical surface, and wherein said diffractive optical element has ameniscus shape and has substantially no total magnifying power.
 2. Thediffractive optical element according to claim 1, wherein said pluralityof phase gratings are of equal width and each of said plurality of phasegratings has a continuous, nonlinear surface to cause phase differencesin a wave front of said incident beam.
 3. The diffractive opticalelement according to claim 2, wherein each of said plurality of phasegratings has an asymmetrical phase pattern, and wherein, a phase gap ΔP,representing a phase difference between an end point of each of saidplurality of phase patterns and a beginning point of each of saidplurality of phase patterns, in radians, is substantially equal for eachof said plurality of phase gratings and satisfies: 0.7π<|ΔP|<1.2π. 4.The diffractive optical element according to claim 3, wherein saidplurality of phase gratings are adjusted so that each of said divideddiffracted beams have substantially the same intensity and no dividedbeam is emitted other than a predetermined number of beams.